Abstract

A vectorial finite-difference time-domain (FDTD) method is used to present a numerical study of very narrow spatial solitons interacting with the surface of what has become known as a left-handed medium. After a comprehensive discussion of the background and the family of surface modes to be expected on a left-handed material, bounded by dispersion-free right-handed material, it is demonstrated that robust outcomes of the FDTD approach yield dramatic confirmation of these waves. The FDTD results show how the linear and nonlinear surface modes are created and can be tracked in time as they develop. It is shown how they can move backward or forward, depending on either a critical value of the local nonlinear conditions at the interface or the ambient linear conditions. Several examples are given to demonstrate the power and versatility of the method and the sensitivity to the launching conditions.